Graphing Techniques
I don't think it's possible for me to overemphasize how important being able to analyze a graph is in AP physics. There are only three things they can ask about a graph on the AP exam:
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1) Determine a data point
2) Determine the slope of the line
3) Determine the area under the graph
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Don't let the simplicity of stating those three things lead you astray. Graphs are complex creatures with hidden attributes. The slope and area are the most important components of a graph in AP Physics.
In AP physics, there are essentially three types of graphs:
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linear - direct relationship - as one thing increases, the other increases in a linear fashion.
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quadratic - as one thing increases, the other also increases in an exponential way.
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inverse or reciprocal - as one thing increases, the other decreases. The line approaches infinity in one direction and zero in the other direction.
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You will primarily see the top 3, although the other two show up on occasion.
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Linear graphs are very common. You see them for Hooke's law, Newton's second law of motion, impulse and momentum and more. Parabolas are also common. You see them for accelerating objects, free fall, energy calculations and the like. Inverse squares are less common but appear for Universal Gravitation, Coulomb's law and the like.
m, the slope of the line should always be something that your recognize - the value for pi, the universal constant for gravity, Planck's constant, the mass of the object, acceleration, gravity, etc. If you don't recognize it, there are techniques for determining what other factors are involved. For example, the slope might be 4pi^2/mass or something similar. That's the harder part of graphing.
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Some things to know for creating a good graph that gets full points:
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Use a grid that scales appropriately. Don't use a tiny graph except in your lab book to simply record the shapes of the graphs. For a lab report or analysis, it needs to be at least half a page in size.
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Scale the axes so that the data fills the entire graph. Don't graph in a corner!
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Label the axes with the variable and what the units for it. Don't abbreviate mass as m or time as t for an analyzed graph.
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Record the shape of the line in words - for example, "parabola arching over the x axis."
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Make a statement about what that means - "as time increases, the distance increases on a square"
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Record the generic equation: "y=mx^2 + b"
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Then linearize the line if necessary and calculate the slope.
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Finally, rewrite the equation with the variables in place and the slope value recorded. Identify the slope.
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You can do the analysis on the graph itself or beneath it. It must be easy to follow.
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So now, you need an example. Practice Graphing